In the context of the gauge/gravity duality, it has been conjectured that the EoP is dual to the entanglement wedge cross-section \(E_w\)  of \(\rho _{AB}\)  which is defined by [1]}, [2]}

Ew(AB)=Area(ABmin)4GN(d+2).

where \(\Sigma _{AB}^{min}\)  is the minimal surface in the entanglement wedge \(E_w(\rho _{AB})\) , separating two regions of A and B, that ends on the RT-surface of \(A\cup B\) , the blue-dashed line in figure REF .
As a result, we have [1]}, [2]}

Ep(AB)Ew(AB).

In order to compute the EoP, we use the holographic prescription given in [1]}, [2]}. We consider two parallel strips with equal widths \(l\)  extended along \(y\)  and \(z\)  directions with length \(L(\rightarrow \infty )\)  and separated by a distance \(l^{\prime }\) , see figure REF . Indeed, in this case \(\Sigma _{AB}^{min}\)  runs along the radial direction and connects the turning points of the minimal surfaces \(\Gamma _{l^{\prime }}\)  and \(\Gamma _{l^{\prime }+2l}\) . In order to obtain the analytical results, we focus in the some specific limits of the our models such as high (\(l^{\prime }\Lambda _c \ \& \ l\Lambda _c \ll 1\) ) and intermediate (\(l^{\prime }\Lambda _c \ll 1\ll l\Lambda _c \) ) energy at zero (\(T=0\) ), low (\(l^{\prime }T \ \& \ lT \ll 1\) ) and intermediate (\(l^{\prime }T \ll 1\ll lT\) ) temperature. In the MAdS background () the high and intermediate energy limits are equivalent to \(r_c\ll r^*_{l^{\prime }} \ \& \ r^*_{l^{\prime }+2l}\)  and \(r_c\ll r^*_{l^{\prime }}\ \& \ r^*_{l^{\prime }+2l}\rightarrow r_c\) , respectively and in the MBH background () the low temperature limit at high and intermediate energy are given in terms of balk parameters as (\(r_c \ \& \ r_H \ll r^*_{l^{\prime }} \ \& \ r^*_{l^{\prime }+2l}\) ) and (\(r_c \ \& \ r_H \ll r^*_{l^{\prime }}\)  and \(r_H\ll r^*_{l^{\prime }+2l}\rightarrow r_c\) ), respectively and the intermediate temperature at high and intermediate energy are given in terms of balk parameters as (\(r_c \ \& \ r_H \ll r^*_{l^{\prime }}\)  and \(r_c\ll r^*_{l^{\prime }+2l}\rightarrow r_H\) ) and (\(r_c \ \& \ r_H \ll r^*_{l^{\prime }}\)  and \(r^*_{l^{\prime }+2l}\rightarrow r_c =r_H\) ), respectively. These regimes are depicted in figure REF .
